
We next use [1]} to develop
an asymptotic expression for
\({\rm {SER}}_{\gamma _{l|S_{l}},{\textrm {MPSK}}}\)  as
\({\rm {SER}}_{{\gamma _{l|{S_l}}},{\rm {MPSK}}}^\infty & \le \frac{\alpha }{\pi }\int _0^{\left( {M - 1} \right)\pi /M} {\prod \limits _{i = 0}^N {\left( {\frac{{{m_i}^{{m_i}}}}{{a_i^{{m_i}}}}{{\left( {\frac{b}{{{{\sin }^2}\theta }}} \right)}^{ - {m_i}}}} \right)} d\theta } \\&= \frac{\alpha }{\pi }\left( {\prod \limits _{i = 0}^N {{{\left( {\frac{{{m_i}}}{{{a_i}b}}} \right)}^{{m_i}}}} } \right)\int _0^{\left( {M - 1} \right)\pi /M} {{{\sin }^{2\sum \nolimits _{i = 0}^N {{m_i}} }}\theta d\theta } \\&= \frac{\alpha }{{\pi {b^{\sum \nolimits _{i = 0}^N {{m_i}} }}}}{A_{M,N}}{\prod \limits _{i = 0}^N {\left( {\frac{{{m_i}}}{{{a_i}}}} \right)} ^{{m_i}}}\) 
